In this article, case-study inverse thermal analyses of Al2198 laser welds are presented. These analyses employ a numerical methodology, that is, in terms of analytic and numerical basis functions for inverse thermal analysis of steady-state energy deposition in plate structures. The results of the case studies presented provide parametric representations of weld temperature histories that can be adopted as input data to various types of computational procedures, such as those for prediction of solid-state phase transformations and their associated software implementations. In addition, these weld temperature histories can be used for construction of numerical basis functions that can be adopted for inverse analysis of welds corresponding to other process parameters or welding processes whose process conditions are within similar regimes.